Transfer-closed characteristicity is transitive

From Groupprops
Jump to: navigation, search
This article gives the statement, and possibly proof, of a subgroup property (i.e., transfer-closed characteristic subgroup) satisfying a subgroup metaproperty (i.e., transitive subgroup property)
View all subgroup metaproperty satisfactions | View all subgroup metaproperty dissatisfactions |Get help on looking up metaproperty (dis)satisfactions for subgroup properties
Get more facts about transfer-closed characteristic subgroup |Get facts that use property satisfaction of transfer-closed characteristic subgroup | Get facts that use property satisfaction of transfer-closed characteristic subgroup|Get more facts about transitive subgroup property


Definition

Suppose H \le K \le G are groups such that K is a transfer-closed characteristic subgroup of G and H is a transfer-closed characteristic subgroup of K. Then, H is a transfer-closed characteristic subgroup of G.

Facts used

  1. Characteristicity is transitive
  2. Transfer condition operator preserves transitivity

Proof

Proof using given facts

The proof follows from facts (1) and (2).

Hands-on proof

PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]